PDF Solutions Manual for Business Math 12th Edition by Cleaves

Chapter 1 Review of Whole Numbers and Integers Section Exercises 1-1, p. 9 1. Twenty-two million, three hundred fifty-six thousand, twenty-seven

2. One hundred six billion, three hundred fifty-seven million, two hundred ninety-one thousand, five hundred eighty-two

3. Seven hundred thirty million, five hundred thirty-one thousand, nine hundred sixty-eight

4. Twenty-one million, seventeen

5. Five hundred twenty-three billion, eight hundred million, seven thousand, one hundred ninety

6. Seven hundred thirteen million, two hundred five thousand, five hundred thirty-eight

7. 14,985

8. 32,943,608

9. 17,000,803,075

10. 50,612,078

11. 306,541

12. 300,760,512

13. 8 is in the tens place. 3 is to its right and is less than 5.

Leave 8 and replace 3 with zero; 480.

14. 7 is in the hundreds place. The digit 6 is on the right and is 5 or more. Add 1 to 7 and replace 6 and 2 with zeros; 3,800.

15. 9 is in the ten-thousands place and 8 is 5 or greater. So 16. 5 is the first digit. 7 is 5 or greater, so add 1 to 5 and increase 9 by 1. Since 9 + 1 = 10, we record 0 and carry replace all digits to its right with zeros; 60,000.

1 to the next place to the left. 2 + 1 = 3. Replace digits to the right of the ten-thousands place with zeros; 300,000.

17. $4,000,000,000

18. $457,025,972,800

19. 0 is in the millions place, 3 on the right is less than 5, so leave 0 as it is and replace all digits on its right with zeros; 860,000,000.

20. 1 is in the first place. The digit to the right, 5, is 5 or more, so round up by adding 1 to the 1 in the first place.

Replace all digits to the right with zeros; 2,000.

21. Negative fifteen thousand, three hundred fourteen dollars 22. Negative eight thousand, four hundred twenty dollars 23. Negative eight thousand, six hundred thirty-six dollars

24. Negative twenty-thousand, one hundred fifty-seven dollars

25. −$520,000,000

26. −$1,800,000,000

1-2, p. 24 1. 300 + 600 + 700 = 1,600; 1,637

2. 700 + 1,000 + 60 = 1,760; 1,710

3. 800 + 1,000 + 50 = 1,850; 1,843

4. 6,000 + 20,000 + 30,000 = 56,000; 53,871

5.

89 −52 37

6.

4 15

5/ 5/ −3 6 19

7.

2 10

3/ 0/ 8 −2 7 5 33

8.

3 10

5, 4/ 0/ 9 −2, 1 7 6 3, 2 3 3

10. 92

11. −8,188

12. −403

13. 21

15. 12

16. −4

17.

18.

×

730 60 43,800

×

9. −6

14. −17 904 24 3 616 18 08 21,696

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19.

×

1, 005 89 9 045 80 40 89,445

1

20. −138 24.

21. −480 25.

16 6 96 6 36 36

27. −8

28. 7

29. −42

35. 2,950 ÷ 50 = 39.

22. 5,312 407 34 13,838 13 6 23 0 238 238

30. −$239

36. 689,100 ÷ 30 =

295 ÷ 5 = 59

68,910 ÷ 3 = 22,970

922 R256 352 324,800 316 8 8 00 7 04 960 704 256

The average selling price of each trailer was nearly $923.

41. 348 ÷ 12 = 29

23. −$580,412 26.

31. 4

260 R4 17 4, 424 34 1 02 1 02 4 0 4

32. $51

37. 57,800,000 ÷ 2,000 =

33. 26

38. 5,730,000 ÷ 300 =

57,800 ÷ 2 = 28,900

40. 8,832 ÷ 8 = 1,104

34. −217 57,300 ÷ 3 = 19,100

Each vendor supplied 1,104 boxes of cards.

42. 21,960 − 16,300 = 5, 660 Visitors increased by 5,660.

You will need 29 boxes.

43. 200, 000, 000 − 500, 000 = 199,500, 000 The sales increase is $199,500,000.

44.

$200,000,000 ÷ $500, 000 = 400 times increase

45. −$39,583 + ( −$23,486 ) =−$63,069

46.

−$32,871 + $29,783 = −$3,088 loss

47. 291× ( −$3) =−$873

48.

−$63,408 ÷ 12 = −$5,284

49. Number of reams in warehouse= 1,358 × 10= 13,580.

If 15,000 reams are needed to process all the store orders, she needs to order more paper.

50.

487 × ( −$12 ) =−$5,844

Exercise Set, p. 32 1. $7,000,000,000

2. 20,000

3. 26

4. 5,400 hotels; 495,000 rooms; 70 countries; 20 percent owned by people from underrepresented groups

5. Negative fourteen billion, six hundred seventy-two million dollars

6. Thirty billion, eight hundred sixty million dollars

7. Negative twenty-seven billion, six hundred eighty-four million dollars

8. Negative eight billion, nine hundred twenty-two million dollars

9. 400

10. 9,000

11. 8,200

12. 350,000

13. 265,472; 2 is in the hundred-thousands place. 6 is to the 14. 3,899; 3 is in the thousands place. 8 is to the right and is right and is more than 5. 300,000. more than 5. $4,000.

6,316,436; 3 is in the hundred-thousands place. 1 is to the right and is less than 5. 6,300,000.

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15. 2,017; 2 is in the thousands place.

0 is to the right and is less than 5.

2,000 radios.

16. $2,499; 4 is in the hundreds place.

9 is to the right and is more than 5. $2,500.

17. 5,000

18. 4,000,000

19. 20,000,000,000

20. 2,000,000

21. 32,948 + 6,804 + 15,695 + 415 + 7,739 = 63,601

22. 47 + 385 + 87 + 439 + 874 = 1,832

23. 46,867 + 7,083 + 723 + 5,209 = 59,882

24. 72 + 385 + 29 + 523 + 816 = 1,825

25. 21,335

4,000 9,000 4,000 + 5,000 22,000

26. 318,936

27. 8,759

3,000 800 4,000 + 600 8,400

28. 2,612

29. 6,288

4,300 600 1,300 + 100 6,300

30. Mental estimation: 90 + 90 + 100 + 90 + 70 + 80 + 60 + 100 = 680 92 + 87 + 96 + 85 + 72 + 84 + 57 + 98 = ⇒ 671 Kiesha had 671 points.

31. Mental estimation: 50 + 100 + 40 + 50 = 240 48 + 96 + 36 + 50 = ⇒ 230 Mary bought 230 items.

70,000 80,000 70,000 + 90,000 310,000 700 900 300 + 700 2,600

32. Mental estimation: 500 + 500 + 500 + 500 + 500 + 100 + 100 = 2,700 483 + 472 + 497 + 486 + 464 + 146 + 87 = ⇒ 2635 The total labor-hours worked was 2,635.

33. Mental estimation: 60 + 40 + 100 + 200 + 300 = 700 57 + 43 + 104 + 210 + 309 = ⇒ 723 Jorge has 723 cards.

34. 4,072

37. 182,902

10,000 − 6,000 4,000

400,000 −200,000 200,000

35. 55,632

80,000 −30,000 50,000

36. 56,539,090

38. 7,310

10,000 − 5,000 5,000

39. 74,385

80,000,000 −30,000,000 50,000,000 100,000 − 40,000 60,000

40. 130 − 42 = ⇒ 88 Sam must order 88 packages.

41. 840 − 596 = ⇒ 244 The number of fan belts to order is 244.

42. 148 − 75 = ⇒ 73 Frieda still has 73 tickets.

43. 132 − 119 = ⇒ 13 Veronica lost 13 pounds.

44. ( −32 ) + ( −27 ) =−59

45. $21 + ( −$47 ) =−$26

46. 14 − ( −12 ) = 14 + 12 = 26

47. −36 − ( −18 ) = −36 + 18 = −18

48. 46 + ( −58 ) =−12

49. $35 + ( −$52 ) =−$17

50. 37 − ( −21)= 37 + 21= 58

51. 72 − ( −42 )= 72 + 42= 114

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3

52.

55.

58.

61.

5,931 835 29 655 177 93 4 744 8 4,952,385

53.

7,870 × 6,000 47,220,000

56.

×

283 3,000 849,000

59.

405 × 400 162,000

×

3,100 500 1,550,000

62.

400 × 500 200,000

×

×

3,128 478 25 024 218 96 1 251 2 1,495,184

×

×

1,987 394 7 948 17883 5961 782,878

54.

5,565 839 50 085 166 95 4 452 0 4,669,035

57.

60.

378 546 2 268 15 12 189 0 206,388

×

64. 28 × 5 =⇒ 140 65. 2017 ÷ 6 = ⇒ 336.1666667 The center requires 140 pieces of There are approximately 336 fruit. radios per thousand people.

67. 793 ÷ 9 = ⇒ 88.11111111 There are approximately 88 TVs per thousand people.

68.

77 16 1,232 1 12 112 112

77 × 16 462 77 1,232

63.

33 × 500 16,500

78,626 87 550 382 6 290 08 6,840,462

×

×

7,000 30 210,000

400 × 70 28,000

×

7,489 34 29 956 224 67 254,626

378 72 756 26 46 27,216

×

= $30; $30 − $27 = $3 66. 2 × $15 Two filters can be purchased at a savings of $3.

69.

8,000 90 748,431

8,805 R6 85 748,431 680 68 4 68 0 43 0 431 425 6

70.

500 300 174,891

505 R161 346 174,891 173 1 89 0 1 891 1 730 161

71.

335 12 4,020 36 42 36 60 60

335 12 670 3 35 4,020

×

72. 483,000 ÷ 3,000= 483 ÷3= 161

73. 73,460,000 ÷10,000 = 7,346 = ÷ 1 7,346

74. 835,000 ÷ 5,000= 835 ÷5= 167

75. 68,650,000 ÷1,000 = 68,650= ÷ 1 68,650

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76. 3,420 ÷ 12 = ⇒ 285 The dealer can make 285 packages.

77. 2,032 ÷ 127 = ⇒ 16 The average hourly wage per employee is $16 per hour.

78. 238 ÷ 2 = ⇒ 119 The stack has 119 countertops.

79. 15 + 32 + 18 + 12 = 77 coins

80. 138 ( −$7 ) = −$966 loss

81. $69,708 ÷ 12 = $5,809 gain

82. −$10,152 ÷ 4 =−$2,538 loss

83. 219 × $3 = $657 gain

84. 34 − 3 × 7 = 34 − 21 = 13

85. ( $32 − $17 + $57 ) ÷ 9= $72 ÷ 9= $8

86. ( −3)( −12 ) − 5 = 36 − 5 = 31

87. ( $72 + $38 − $21 + $32 ) ×= 3 $121×= 3 $363

88. 63 + 126 ÷ 7 = 63 + 18 = 81

89. ( −5 )( −11) − 18 = 55 − 18 = 37

Practice Test, p. 36 1. five hundred three

2. twelve million, fifty-six thousand, thirty-nine

3. 80,000

4. 600,000

5. 5,017,135,632

6. 17,500,608

7. Twenty-two billion, six hundred ninety-seven million dollars

8. Eighty-seven billion, four hundred seventy-one million, nine hundred thousand dollars

9.

11. −21

12. −23

14. −8 − 21 =−8 + ( −21) =−29

15.

17. 438 + 72 + 643 = ⇒ 1153 1,153 items were counted.

18. 31 ÷ 2 = ⇒ 15.5 Only 15 boxes can be stacked.

19. 2988 ÷ 12 = ⇒ 249 249 packages can be made.

20. 43 − 23 = ⇒ 20 20 pairs of shoes remain in inventory.

21. 680 ÷ 40 = ⇒ 17 She makes $17 per hour.

22. 28 × 2 = ⇒ 56

23. 16 × 3 =⇒ 48 48 pages are devoted to review.

24. 48 − 11 = ⇒ 37 37 novels were received.

10.

1,000 − 300 700

987 − 346 641

13. 5 − 32 =5 + ( −32 ) =−27

16.

80 50 4,021

75 R46 53 4,021 3 71 311 265 46

56 × 5 =⇒ 280 280 pieces of fruit are required.

900 1,000 + 300 2,200

900 × 50 45,000

863 983 + 271 2,117

892 46 5 352 35 68 41,032

×

25. $23,522,400,000 − $4,313,200,000 = $19,209,200,000 = ,200,000 − ( −$394,900,000 ) 26. Loss negative profit; $34,362 $34,362,200,000 + $394,900,000 = $34,757,100,000

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27. −$8,915 + ( −$5,212 ) + ( −$6,103) =−$20,230 29. 186 × ( −$11) =−$2,046

28. −$15,814 − ( −$7,928 ) = −$15,814 + $7,928 = −$7,886 31. 133 ÷ 7 × ( −4 ) + 26 = 19 × ( −4 ) + 26 = −76 + 26 = −50

30. −$26,136 ÷ 12 = −$2,178

32. ( $68 + $52 − $71 + $32 ) × 9= $81× 9= $729

Critical Thinking, p. 38 1. = n 17 − 12 n=5

2. = n 45 ÷ 5 n=9

3. Answers will vary.

(12 − 5) − 2 = 7 − 2 = 5 12 − ( 5 − 2 ) = 12 − 3 = 9

4. Answers will vary.

8÷4 = 4 4 = 4 ÷8 does = not 4 8

5. Answers will vary. You made purchases of $15 and $18.

What is the total of your purchases?

6. Answers will vary. You purchased seven items that cost $23 each. What is the total of your purchases?

7. Answers will vary. Multiplication 4 + 4 + 4 + 4 += 4 5 ( 4= ) 20.

8. Addition and Subtraction

9. Division

zero missing 10.

11. 5 + 3 ( 8 ) − 12 =

12. 25 − 12 + 7 = 13 + 7 = 20 5 + 24 − 12 = Addition and subtraction must 29 − 12 = 17 be completed in the order they The order of operations requires occur, working from left to multiplication to be completed before right. addition or subtraction.

59 12 6,108 60 108 108

509 12 6,108 60 10 0 108 108 The 5 in the quotient should align above the 1 in the dividend.

Combining Concepts, p. 38 1.

120 135 + 165 420

500 − 420 80 units

2.

TABLE 1-2 Employee Name Brown, Tyler Lopez, Cierra Prete, Aaron Salayon, Steven Vidrine, Stephen Waddell, Dawn Young, Travon

Week 1 15 23 18 21 31 17 15

Week 2 12 18 19 15 12 18 19

Week 3 23 14 27 16 9 12 14

Week 4 27 12 9 17 15 21 13

Units Sold 77 67 73 69 67 68 61

The overall monthly sales were 482 units. The monthly quota of 500 units was not reached. Tyler Brown and Aaron Prete reached their monthly sales goals.

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3.

TABLE 1-3 Region Eastern Southern Central Western Daily Sales Total

W Th F S $72,492 $81,948 $32,307 $24,301 81,897 59,421 48,598 61,025 71,708 22,096 23,222 21,507 61,723 71,687 52,196 41,737 $287,820 $235,152 $156,323 $148,570

Su $32,589 21,897 42,801 22,186 $119,473

Region Totals $243,637 272,838 181,334 249,529 $947,338

Region Totals = $243, 637 + $272,838 + $181,334 + $249,529 = $947,338 Difference =Goal − Actual =$1,384, 000 − $947,338 = $436, 662 Daily Sales Totals = $287,820 + $235,152 + $156,323 + $148,570 + $119,473 + $947,338 Goal was not reached.

4.

Total pounds of candy = 84 × 25 = 2,100 Number of bags of candy 3 700 = 2,100 ÷= Number of boxes of candy = 700 ÷ 12 = 58 R4 There are 58 boxes of candy and 4 bags left so 59 boxes will be needed to ship all the candy. Enough bags and boxes are on hand to package.

5.

Total length of fencing needed= 210 × 4= 840 feet Number of rolls of fencing needed = 840 ÷ 50 = 16 R40 Because a partial roll of fencing cannot be purchased, 17 rolls are needed.

Cost of 17 rolls of fencing = $49 × 17 = $833 Cost of installing fence =$1× 840 =$840 Total cost = $833 + $840 = $1, 673 Your bid is the lowest bid and you are likely to get the business.

6.

Wages =3 × $15 × 21 =$945 Gross proft = total − cost of materials − cost of labor Gross proft= $1,673 − $833 − $945= $105

7.

12 + 27 + 55 + 21 = 115 gallons; yes, 100 gallons of fuel can be stored in these containers.

8.

$75 + $45 + 4($10) = $75 + $45 + $40 = $160; $160 − $7 = $153

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Case Studies 1-1, p. 41 1. Daily Pass: 250 days × $6 = $1, 500 $1,500 − $1,260 = $240

Monthly Pass: 12 months × $105 = $1,260

2. Daily Mileage: 2 × 20 miles= = 40 miles 40 miles 1= gallon of gasoline per day $4 Annual Fuel Cost: $4 × 250 days = $1, 000 Parking Cost: $120 × 50 weeks = $6, 000 $7, 000 Cost to Drive to Work: $1,000 + $6,000 = 3. Position 1 is $70,000 per year; $70, 000 − $1, 260 (annual cost of bus) = $68, 740 Position 2 is $67,000 per year; $67, 000 + $2, 000 (wellness bonus) = $69, 000 Position 2 is the better option.

1-2, p. 42 1. 45 ft × 20 ft × 2 sides = 1,800 ft 2 1,800 ft 2 ÷ 100 = 18 roofing squares For the roof, 1,800 ft 2 of roofing is required, which is 18 roofing squares.

72 bundles 2. 18 squares × 4 bundles = 18 squares ÷3 =6 rolls of roofing felt 72 bundles × $42 per bundle = $3,024 total shingle cost 6 rolls × $27 per roll = $162 total roofing felt cost For the roof, 72 bundles of shingles are needed at a cost of $3,024. Also, 6 rolls of felt are needed at a cost of $162.

3.

18 squares ÷ 3 squares = 6 boxes; 6 boxes × $15 = $90 nail cost

85 ft per side of drip edge ( 20 ft + 20 ft + 45 ft ) =

17 drip edge pieces × $6 per = $102 total drip edge cost Total cost = $3,024 + $162 + $90 + $102 = $3,378

85 ft × 2 sides = 170 ft; 170 ft ÷ 10 ft length = 17 pieces 6 boxes of roofing nails are needed at a cost of $90; 17 lengths of drip edge are needed at a cost of $102. The material costs for the entire roof are $3,378.

1-3, p. 42 1. 150 + 75 + 25 = 250 people $100, 000 ÷ 250 = $400 2. $400 ÷ 10 = $40 3. First shift: 100 ( $40 25 ( $100 ) $2,500; 15 ( $50 ) $750; = = = )(10 months ) $40,000; 10 (= $20 )(10 ) $2,000; $40,000 + $2,500 + $750= + $2,000 $45,250 total Second= shift: 25 ( $150 ) $3,750; = 25 ( $40 )(10 ) $10,000; = 25 ( $35 ) $875 $3,750 + $10,000 + $875 = $14,625 total Third shift: 25 ( $80 )(10 ) = $20,000 total 4. No, she is short $20,125. $45,250 + $14,625 += $20,000 $79,875; $100,000 −= $79,875 $20,125 5. $79,875 ( 2 ) = $159,750 company contribution

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Chapter 1

$79,875 + $159,750 = $239,625 total contribution

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